Various abrasive articles and methods for the lapping of substrates, e.g. hard substrates, have been disclosed in the art. Such articles and methods are described in, for example, U.S. Pat. Nos. 7,169,031, 7,494,519 and 7,594,845. Lapping is a grinding process that typically involves a slurry of loose abrasive grits, such as aluminum oxide in a liquid, flowed across a rotating lap plate, typically a metal such as cast iron. This provides an abrasive film between the polishing pad and the workpiece that enables stock removal from a single side or from both sides simultaneously. Lapping may also be conducted using fixed abrasive pads, often in combination with a liquid coolant or lubricant to facilitate the lapping process.